Force on 1 point charge in a 4 point charge system

In summary, we use the formula F=k(q1q2/r^2) to find the magnitude of the total force exerted on one charge by the other three charges, where Q represents the charge and L represents the side length of the square. In the solution, the L root2 comes from resolving the diagonal force along the south and west directions. This results in a net force of kQ^2[1+2root2]/2L^2. We can also use Pythagoras theorem to find the diagonal of the cube.
  • #1
Josh930
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Homework Statement



Four identical charges are placed at the corners of a square of side side L.
Find the magnitude total force exerted on one charge by the other three charges.
Express your answer in terms of the variables Q, L and appropriate constants.

where did the L root2 in the solution come from?


Homework Equations



F=k(q1q2/r^2)





The Attempt at a Solution



let the charge Q at bottom left corner be considered, it is ready to move under repulsion

f1 = F(top, bottom) = kQ^2/L^2 [south] = x
f2=F(right, bottom) = kQ^2/L^2 [west] = x
f3 = F(diagonal, bottom) = kQ^2/[L root2]^2 [south-west]
f3 = x/2
--------------------------------------…
resolve f3 along south & west

F(net south) = x + [x/2] cos 45 = x[1+ 1/2root2]
F(net south) = x[1+2root2] /2root2 = F
F(net west) = x[1+2root2] /2root2 =F

F(resultant) = sqrt[F^2 + F^2] = F root2
F(resultant) = [ x[1+2root2] /2root2 ][root2]
F(resultant) = x[1+2root2] /2
F(resultant) = kQ^2[1+2root2] /2L^2
 
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  • #2
Use Pythagoras theorem to find the diagonal of the cube.
 
  • #3


In response to the question about the L root2 in the solution, the L root2 comes from the diagonal force f3 which was resolved into components along the south and west directions. This is because the diagonal force is acting at a 45 degree angle, so it needs to be broken down into its components in order to be added to the other forces acting on the charge. This is a common technique used in vector addition and can be seen in the homework equations provided. The L root2 term is then squared in the final solution because it is in the denominator of the distance term in the force equation, resulting in an L^2 term. I hope this explanation helps clarify the solution for you.
 

1) What is the formula for calculating the force on a point charge in a 4 point charge system?

The formula for calculating the force on a point charge in a 4 point charge system is F = k(q1q2/r^2), where k is the Coulomb's constant, q1 and q2 are the charges of the two interacting point charges, and r is the distance between them.

2) How does the direction of the force on a point charge in a 4 point charge system depend on the location of the charge?

The direction of the force on a point charge in a 4 point charge system depends on the relative positions of the charges. If the charges are arranged symmetrically, the force will be directed towards the center of the system. If the charges are not symmetrically arranged, the force may be directed at an angle towards the center or away from it.

3) Can the force on a point charge in a 4 point charge system ever be zero?

Yes, the force on a point charge in a 4 point charge system can be zero if the charges are arranged in a way that the forces acting on the charge cancel each other out. This can happen if the charges are equally spaced and have equal magnitude.

4) How does the force on a point charge change if the distance between the charges is increased?

The force on a point charge follows an inverse square relationship with the distance between the charges. This means that as the distance between the charges increases, the force on the point charge decreases. If the distance is doubled, the force becomes one-fourth of its original value.

5) Is the force on a point charge in a 4 point charge system affected by the charges' electric fields?

Yes, the force on a point charge in a 4 point charge system is affected by the electric fields of the other charges. The presence of electric fields can either strengthen or weaken the force on the point charge, depending on the direction and strength of the fields.

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